Answer: (V 0 I 0 /2) cos(φ).
- A (V<sub>0</sub> I<sub>0</sub>/2) cos(φ)
- B V<sub>0</sub> I<sub>0</sub> cos(φ)
- C (V<sub>0</sub> I<sub>0</sub>/2) sin(φ)
- D 0
Correct answer: A. (V<sub>0</sub> I<sub>0</sub>/2) cos(φ)
Explanation: Instantaneous power p = VI = V<sub>0</sub> I<sub>0</sub> cos(ωt) cos(ωt + φ). Time average gives: P<sub>avg</sub> = (V<sub>0</sub> I<sub>0</sub>/2) cos(φ) = V<sub>rms</sub> I<sub>rms</sub> cos(φ).
In a pure inductor the current lags the voltage by 90° (energy is briefly stored in the magnetic field before current responds); in a pure capacitor the current leads the voltage by 90° (current must flow to build up charge before voltage rises) - the mnemonic "ELI the ICE man" keeps these straight.
Concept context
AC circuits, impedance, LCR series circuit, resonance, transformers, and power factor.